The SUTRA dispersion model in three dimensions (3D) is a
generalization of the original two-dimensional (2D) model. The 2D and 3D SUTRA
dispersion models are described in detail in Section 2.5 of the SUTRA
documentation. This page supplements the formal documentation by providing
interactive visualizations of the 3D dispersion model. A VRML
browser is required to view the visualizations
interactively.

In the 3D SUTRA dispersion model, the longitudinal and transverse
dispersivities,
aL, aT1,
and aT2, can depend on the direction
of groundwater flow, i.e., the dispersion model can be anisotropic. SUTRA
computes the value of the longitudinal dispersivity, aL,
from the radius of an ellipsoid measured along the flow direction. Thus, aL
is greatest when flow is along the longest axis of the ellipsoid. The transverse
dispersivities, aT1
and aT2, are computed from radii of a
second ellipsoid. These transverse radii are measured along two directions that
are perpendicular to the flow direction and to each other.

The user controls the behavior of the 3D dispersion model by setting SUTRA
input parameters that determine the dimensions and orientation of the two
ellipsoids in space:

For simplicity, both dispersivity ellipsoids are oriented with their
principal axes aligned with the principal permeability directions, i.e.,
with the maximum (max), middle (mid), and minimum (min) permeability
directions defined by the angles ANGLE1, ANGLE2, and ANGLE3 in dataset 15.

The dimensions of the longitudinal dispersivity ellipsoid are determined
by the dispersivities ALMAX, ALMID, and ALMIN in dataset 15. The principal
radii in the max, mid, and min directions are (aLmax)1/2,
(aLmid)1/2,
and (aLmin)1/2, respectively,
where aLmax, aLmid,
and aLmin
represent ALMAX, ALMID, and ALMIN, respectively.

The dimensions of the transverse dispersivity ellipsoid are determined by
the dispersivities ATMAX, ATMID, and ATMIN in dataset 15. The principal
radii in the max, mid, and min directions are (aTmax)1/2,
(aTmid)1/2,
and (aTmin)1/2, respectively,
where aTmax, aTmid,
and aTmin represent ATMAX, ATMID, and
ATMIN, respectively.

Figure. How SUTRA
calculates the longitudinal dispersivity, aL,
as a function of flow direction. Here, v is the flow (velocity) vector; xmax,
xmid, and xmin are coordinates aligned with the max, mid,
and min directions, respectively; and aL
is the squared radius measured along the flow direction. The principal radii of
the ellipsoid (not labeled) have squared lengths of aLmax,
aLmid, and aLmin,
and are aligned with the max, mid, and min directions, respectively. Note that aL=aLmax
for flow in the max direction, aL=aLmid
for flow in the mid direction, and aL=aLmin
for flow in the min direction.

The way in which SUTRA computes the transverse dispersivities, aT1
and aT2, as a functions of flow direction
is illustrated in the figure below, which corresponds to Figure 2.4c in the SUTRA
documentation:

Figure. How SUTRA
computes the transverse dispersivities, aT1
and aT2, as a functions of flow direction. Here, v is the flow (velocity)
vector and xmax,
xmid, and xmin are coordinates aligned with the max, mid,
and min directions, respectively. The principal radii of the ellipsoid (not labeled) have
squared lengths of aLmax, aLmid,
and aLmin, and are aligned with the max,
mid, and min directions, respectively; and aT1
and aT2 are squared radii measured in two
directions perpendicular to the flow direction. These two directions,
which are the transverse dispersion directions, correspond to the principal axes of the ellipse (called the slicing ellipse) formed
by the intersection of the ellipsoid with the plane that passes through the
origin and is perpendicular to the
flow direction. Note that when groundwater flow is in one of the three principal permeability
directions (max, mid, or min), aT1
and aT2 take on the values associated with the
other two
directions. Thus, the transverse dispersivities are aTmid
and aTmin for flow in the max
direction; aTmax and aTmin
for flow in the mid direction; aTmax
and aTmid for flow in the min
direction.